20 ( +1 | -1 ) I've no idea, and no-one else seems to either. It can be seen as an anti-Ruy Lopez opening compared to 2. Nc6 (meaning 3. Bb5 is good against 2. Nc6, but not against 2.d6.) Other than that, it's difficult to see what benefits it brings.
116 ( +1 | -1 ) The Philidor most certainly makes sense, it's just a question of whether the plan involved is actually good enough.
The whole idea is to build a very solid position. The pawn on d6 supports the e5 pawn and allows black to maintain a pawn in the center following dxe5 ...dxe5. Black develops his pieces into a cramped position, but this almost dares white to try to tear it all down, if he can. The bishop is ok on e7, where it serves some defensive roles and can relocate when necessary.
Also, black gets some initiative on the queenside sometimes. Other times, black will play 1. e4 e5 2. Nf3 d6 3. d4 exd4 4. Nxd4 g6 -- ceding the center but opening up for a fianchettoed bishop.
There's also another plan for black given on this site: www.vanrekom.nl (it's easier to just look at the diagrams and variations there then for me to repeat it all here). It's more aggressive, pushing forward on the kingside while hoping that the center and queenside hold strongly enough to keep black from collapsing.
35 ( +1 | -1 ) "What does the Lion have to do with the Philidor? "
The Lion is a variation of the Philidor. You can reach the Philidor via the Pirc move order, and then go for the whole Lion thing.
In any event, after 1. e4 e5 2. Nf3 d6 you have the Philidor, and then you could continue with 3. d4 Nf6 4. Nc3 Nbd7 5. Bc4 Be7 6. O-O (still all Philidor territory) and now 6...h6, preparing the whole Lion thing with ...c6, ...Qc7, ...g4, etc.